Kernelized cost-sensitive listwise ranking

Learning to Rank is an area of application in machine learning, typically supervised, to build ranking models for Information Retrieval systems. The training data consists of lists of items with some partial order specified induced by an ordinal or binary score. The model purpose is to produce a permutation of the items in this list in a way which is close to the rankings in the training data. This technique has been successfully applied to ranking, and several approaches have been proposed since then, including the Listwise approach. A cost-sensitive version of that is an adaptation of this framework which treats the documents within a list with different probabilities, i.e., attempt to impose weights for the documents with higher cost. We then take this algorithm to the next level by kernelizing the loss and exploring the optimization in different spaces. Among the different existing likelihood algorithms, we choose ListMLE as pri- mary focus of experimentation, since it has been shown to be the approach with the best empirical performance. The theoretical framework is given along with its mathematical properties